# Hypothesis Testing Model

Updated on October 25, 2014

## Hypothesis Testing Model

Hypothesis testing is used by researchers in a variety of quantitative research studies to prove or disprove a theory. Hypothesis testing is a “procedure for deciding whether the outcome of a study (results for a sample) supports a particular theory or practical innovation” (Aron, Coups, & Aron, 2013, p. 108). There are five main steps for organizing hypothesis testing: restate the question as a research hypothesis and a null hypothesis about the populations, determine the characteristics of the comparison distribution, determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected, determine the sample’s score on the comparison distribution, and decide whether to reject the null hypothesis.

The first step for organizing a hypothesis test is to restate the question as a research hypothesis and a null hypothesis about the populations. The research hypothesis is a “statement in hypothesis testing about the predicted relation between populations” (Aron, Coups, & Aron, 2013, p. 111). The null hypothesis is a “statement about a relation between populations that is the opposite of the research hypothesis” (Aron, Coups, & Aron, 2013, p. 111). The second step is to determine the characteristics of the comparison distribution; comparison distribution represents the population situation if the null hypothesis were to be proven correct (Aron, Coups, & Aron, 2013, p. 112). During this step the comparison distribution is compared with the score that came from the results of the sample. The third step is to determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected; the cutoff sample score, also known as the critical value, is the “point in hypothesis testing, on the comparison distribution at which, if reached or exceeded by the sample score, you reject the null hypothesis” (Aron, Coups, & Aron, 2013, p. 112). During this step researchers decide how extreme a score must be for the score to be too implausible for the null hypothesis to be true. The fourth step is to determine the sample’s score on the comparison distribution; this is the step where the study is carried out, the results of the sample are collected, and the z-score for the sample’s raw score is determined based on the standard deviation of the comparison distribution and the population mean (Aron, Coups, & Aron, 2013, p. 114). The fifth and final step is to decide whether to reject the null hypothesis; this is done by comparing the sample’s Z score to the cutoff Z score in order to decide if the null hypothesis is accepted or rejected.

Hypothesis testing is mainly used by researchers in order to determine if a theory or hypothesis is accurate or inaccurate through statistical testing. The five step model of hypothesis testing has the advantage of: being simple to calculate, working with most quanataive research, being suited for comparisons, and providing provable rational results that decisively reject or accept the research hypothesis and the null hypothesis about the population.

## Reference

Aron, A., Aron. E., Coups. E. (2014). Statistics for Psychology Pearson Education Inc. 2014.

## Chapter 11: Correlation

Correlation

Association between scores on two variables

e.g., age and coordination skills in children, price and quality

Graphing Correlations
The Scatter Diagram

Steps for making a scatter diagram

1. Draw axes and assign variables to them

2. Determine range of values for each variable and mark on axes

3. Mark a dot for each person’s pair of scores

Graphing Correlations
The Scatter Diagram

Graphing Correlations: The Scatter Diagram

Patterns of Correlation

Linear correlation

Curvilinear correlation

No correlation

Positive correlation

Negative correlation

Degree of Linear Correlation
The Correlation Coefficient

Figure correlation using Z scores

Cross-product of Z scores

Multiply Z score on one variable by Z score on the other variable

Correlation coefficient

Average of the cross-products of Z scores

Degree of Linear Correlation
The Correlation Coefficient

General formula for the correlation coefficient:

Positive perfect correlation: r = +1

No correlation: r = 0

Negative perfect correlation: r = –1

Correlation and Causality

Three possible directions of causality:

1. X Y

2. X Y

3. Z

X Y

Correlation and Causality

Correlational research design

Correlation as a statistical procedure

Correlation as a research design

Issues in Interpreting the Correlation Coefficient

Statistical significance

Proportionate reduction in error

r2

Used to compare correlations

Restriction in range

Unreliability of measurement

Curvilinearity

Spearman’s rho

Power for Studies Using
Correlation Coefficient
(.05 significance level)

Table indicated below here

Approximate Sample Size for
80% Power for Correlation Studies (.05 significance level)

Table indicated below here

Correlation in Research Articles

Scatter diagrams occasionally shown

Correlation matrix

2

4

1

0

3

2

3